Joint sequence estimation of symbol and phase with high tolerance of nonlinearity

ABSTRACT

A method and system for a sequence estimation in a receiver, such as for use when receiving a sample of a received inter-symbol correlated (ISC) signal corresponding to a transmitted vector of L symbols, with L being a integer greater than 1, and with symbol L being a most-recent symbol and symbol 1 being least recent symbol of the vector. A plurality of candidate vectors may be generated, wherein element L−m of each candidate vector holding one of a plurality of possible values of the symbol L−m, with m is an integer greater than or equal to 1, and elements L−m+1 through L of each candidate vectors holding determined filler values. A plurality of metrics may be generated based on the plurality of candidate vectors, and based on the generated plurality of metrics, a best one of the possible values of the symbol L−m may be selected.

CLAIM OF PRIORITY

This patent application is a continuation of U.S. patent applicationSer. No. 13/755,043 filed on Jan. 31, 2013 (now patented as U.S. Pat.No. 8,605,832), which in turn, claims priority to U.S. ProvisionalPatent Application Ser. No. 61/662,085 titled “Apparatus and Method forEfficient Utilization of Bandwidth” and filed on Jun. 20, 2012, U.S.Provisional Patent Application Ser. No. 61/726,099 titled “ModulationScheme Based on Partial Response” and filed on Nov. 14, 2012, and U.S.Provisional Patent Application Ser. No. 61/729,774 titled “ModulationScheme Based on Partial Response” and filed on Nov. 26, 2012. Thisapplication is also a non-provisional of U.S. Provisional PatentApplication Ser. No. 61/747,132 titled “Modulation Scheme Based onPartial Response” and filed on Dec. 28, 2012.

Each of the above-identified applications is hereby incorporated hereinby reference in its entirety.

INCORPORATION BY REFERENCE

This application makes reference to:

U.S. patent application Ser. No. 13/754,998, titled “Design andOptimization of Partial Response Pulse Shape Filter,” and filed on Jan.31, 2013;

U.S. patent application Ser. No. 13/755,001, titled “Constellation MapOptimization For Highly Spectrally Efficient Communications,” and filedon Jan. 31, 2013;

U.S. Pat. No. 8,571,131, titled “Dynamic Filter Adjustment forHighly-Spectrally-Efficient Communications,” and filed on Jan. 31, 2013;

U.S. Pat. No. 8,559,494, titled “Timing Synchronization for Reception ofHighly-Spectrally-Efficient Communications,” and filed on Jan. 31, 2013;

U.S. Pat. No. 8,599,914, titled “Feed Forward Equalization forHighly-Spectrally-Efficient Communications,” and filed on Jan. 31, 2013;

U.S. patent application Ser. No. 13/755,021, titled “Decision FeedbackEqualizer for Highly-Spectrally-Efficient Communications,” and filed onJan. 31, 2013;

U.S. patent application Ser. No. 13/755,025, titled “Decision FeedbackEqualizer with Multiple Cores for Highly-Spectrally-EfficientCommunications,” and filed Jan. 31, 2013;

U.S. Pat. No. 8,559,498, titled “Decision Feedback Equalizer UtilizingSymbol Error Rate Biased Adaptation Function forHighly-Spectrally-Efficient Communications,” and filed on Jan. 31, 2013;

U.S. Pat. No. 8,548,097, titled “Coarse Phase Estimation forHighly-Spectrally-Efficient Communications,” and filed on Jan. 31, 2013;

U.S. Pat. No. 8,565,363, titled “Fine Phase Estimation for HighlySpectrally Efficient Communications,” and filed on Jan. 31, 2013.

Each of the above stated applications is hereby incorporated herein byreference in its entirety.

TECHNICAL FIELD

Aspects of the present application relate to electronic communications.More specifically, certain implementations of the present disclosurerelate to joint sequence estimation of symbol and phase with hightolerance of nonlinearity.

BACKGROUND

Existing communications methods and systems are overly power hungryand/or spectrally inefficient. Further limitations and disadvantages ofconventional and traditional approaches will become apparent to one ofskill in the art, through comparison of such approaches with someaspects of the present method and system set forth in the remainder ofthis disclosure with reference to the drawings.

BRIEF SUMMARY

Methods and systems are provided for joint sequence estimation of symboland phase with high tolerance of nonlinearity, substantially asillustrated by and/or described in connection with at least one of thefigures, as set forth more completely in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram depicting an example system configured forlow-complexity, highly-spectrally-efficient communications.

FIG. 2 is a block diagram depicting an example equalization and sequenceestimation circuit for use in a system configured for low-complexity,highly-spectrally-efficient communications.

FIG. 3 is a block diagram depicting an example sequence estimationcircuit for use in a system configured for low-complexity,highly-spectrally-efficient communications.

FIG. 4 is a block diagram depicting an example metrics calculationcircuit for use in a system configured for low-complexity,highly-spectrally-efficient communications.

FIGS. 5A-5E depict portions of an example sequence estimation processperformed by a system configured for joint sequence estimation of symboland phase with high tolerance of nonlinearity.

FIG. 6 is a flowchart illustrating an example process for sequenceestimation, with high tolerance of nonlinearity, for reception ofpartial response signals.

DETAILED DESCRIPTION

As utilized herein the terms “circuits” and “circuitry” refer tophysical electronic components (i.e. hardware) and any software and/orfirmware (“code”) which may configure the hardware, be executed by thehardware, and or otherwise be associated with the hardware. As usedherein, for example, a particular processor and memory may comprise afirst “circuit” when executing a first plurality of lines of code andmay comprise a second “circuit” when executing a second plurality oflines of code. As utilized herein, “and/or” means any one or more of theitems in the list joined by “and/or”. As an example, “x and/or y” meansany element of the three-element set {(x), (y), (x, y)}. As anotherexample, “x, y, and/or z” means any element of the seven-element set{(x), (y), (z), (x, y), (x, z), (y, z), (x, y, z)}. As utilized herein,the terms “block” and “module” refer to functions than can be performedby one or more circuits. As utilized herein, the term “exemplary” meansserving as a non-limiting example, instance, or illustration. Asutilized herein, the terms “for example” and “e.g.,” introduce a list ofone or more non-limiting examples, instances, or illustrations. Asutilized herein, circuitry is “operable” to perform a function wheneverthe circuitry comprises the necessary hardware and code (if any isnecessary) to perform the function, regardless of whether performance ofthe function is disabled, or not enabled, by some user-configurablesetting.

FIG. 1 is a block diagram depicting an example system configured forlow-complexity, highly-spectrally-efficient communications. The system100 comprises a mapper circuit 102, a pulse shaping filter circuit 104,a timing pilot insertion circuit 105, a transmitter front-end circuit106, a channel 107, a receiver front-end 108, a filter circuit 109, atiming pilot removal circuit 110, an equalization and sequenceestimation circuit 112, and a de-mapping circuit 114. The components102, 104, 105, and 106 may be part of a transmitter (e.g., a basestation or access point, a router, a gateway, a mobile device, a server,a computer, a computer peripheral device, a table, a modem, a set-topbox, etc.), the components 108, 109, 110, 112, and 114 may be part of areceiver (e.g., a base station or access point, a router, a gateway, amobile device, a server, a computer, a computer peripheral device, atable, a modem, a set-top box, etc.), and the transmitter and receivermay communicate via the channel 107.

The mapper 102 may be operable to map bits of the Tx_bitstream to betransmitted to symbols according to a selected modulation scheme. Thesymbols may be output via signal 103. For example, for an quadratureamplitude modulation scheme having a symbol alphabet of N (N-QAM), themapper may map each Log₂(N) bits of the Tx_bitstream to single symbolrepresented as a complex number and/or as in-phase (I) andquadrature-phase (Q) components. Although N-QAM is used for illustrationin this disclosure, aspects of this disclosure are applicable to anymodulation scheme (e.g., amplitude shift keying (ASK), phase shiftkeying (PSK), frequency shift keying (FSK), etc.). Additionally, pointsof the N-QAM constellation may be regularly spaced (“on-grid”) orirregularly spaced (“off-grid”). Furthermore, the symbol constellationused by the mapper may be optimized for best bit-error rate performancethat is related to log-likelihood ratio (LLR) and to optimizing meanmutual information bit (MMIB). The Tx_bitstream may, for example, be theresult of bits of data passing through a forward error correction (FEC)encoder and/or an interleaver. Additionally, or alternatively, thesymbols out of the mapper 102 may pass through an interleaver.

The pulse shaper 104 may be operable to adjust the waveform of thesignal 103 such that the waveform of the resulting signal 113 complieswith the spectral requirements of the channel over which the signal 113is to be transmitted. The spectral requirements may be referred to asthe “spectral mask” and may be established by a regulatory body (e.g.,the Federal Communications Commission in the United States or theEuropean Telecommunications Standards Institute) and/or a standards body(e.g., Third Generation Partnership Project) that governs thecommunication channel(s) and/or standard(s) in use. The pulse shaper 104may comprise, for example, an infinite impulse response (IIR) and/or afinite impulse response (FIR) filter. The number of taps, or “length,”of the pulse shaper 104 is denoted herein as LTx, which is an integer.The impulse response of the pulse shaper 104 is denoted herein as hTx.The pulse shaper 104 may be configured such that its output signal 113intentionally has a substantial amount of inter-symbol interference(ISI). Accordingly, the pulse shaper 104 may be referred to as a partialresponse pulse shaping filter, and the signal 113 may be referred to asa partial response signal or as residing in the partial response domain,whereas the signal 103 may be referred to as residing in the symboldomain. The number of taps and/or the values of the tap coefficients ofthe pulse shaper 104 may be designed such that the pulse shaper 104 isintentionally non-optimal for additive white Gaussian noise (AWGN) inorder to improve tolerance of non-linearity in the signal path. In thisregard, the pulse shaper 104 may offer superior performance in thepresence of non-linearity as compared to, for example, a conventionalnear zero positive ISI pulse shaping filter (e.g., root raised cosine(RRC) pulse shaping filter). The pulse shaper 104 may be designed asdescribed in one or more of: the United States patent application titled“Design and Optimization of Partial Response Pulse Shape Filter,” theUnited States patent application titled “Constellation Map OptimizationFor Highly Spectrally Efficient Communications,” and the United Statespatent application titled “Dynamic Filter Adjustment ForHighly-Spectrally-Efficient Communications,” each of which isincorporated herein by reference, as set forth above.

It should be noted that a partial response signal (or signals in the“partial response domain”) is just one example of a type of signal forwhich there is correlation among symbols of the signal (referred toherein as “inter-symbol-correlated (ISC) signals”). Such ISC signals arein contrast to zero (or near-zero) ISI signals generated by, forexample, raised-cosine (RC) or root-raised-cosine (RRC) filtering. Forsimplicity of illustration, this disclosure focuses on partial responsesignals generated via partial response filtering. Nevertheless, aspectsof this disclosure are applicable to other ISC signals such as, forexample, signals generated via matrix multiplication (e.g., latticecoding), and signals generated via decimation below the Nyquistfrequency such that aliasing creates correlation between symbols.

The timing pilot insertion circuit 105 may insert a pilot signal whichmay be utilized by the receiver for timing synchronization. The outputsignal 115 of the timing pilot insertion circuit 105 may thus comprisethe signal 113 plus an inserted pilot signal (e.g., a sine wave at¼×fbaud, where fbaud is the symbol rate). An example implementation ofthe pilot insertion circuit 105 is described in the United States patentapplication titled “Timing Synchronization for Reception ofHighly-Spectrally-Efficient Communications,” which is incorporatedherein by reference, as set forth above.

The transmitter front-end 106 may be operable to amplify and/orupconvert the signal 115 to generate the signal 116. Thus, thetransmitter front-end 106 may comprise, for example, a power amplifierand/or a mixer. The front-end may introduce non-linear distortion and/orphase noise (and/or other non-idealities) to the signal 116. Thenon-linearity of the circuit 106 may be represented as FnlTx which maybe, for example, a polynomial, or an exponential (e.g., Rapp model). Thenon-linearity may incorporate memory (e.g., Voltera series).

The channel 107 may comprise a wired, wireless, and/or opticalcommunication medium. The signal 116 may propagate through the channel107 and arrive at the receive front-end 108 as signal 118. Signal 118may be noisier than signal 116 (e.g., as a result of thermal noise inthe channel) and may have higher or different ISI than signal 116 (e.g.,as a result of multi-path).

The receiver front-end 108 may be operable to amplify and/or downconvertthe signal 118 to generate the signal 119. Thus, the receiver front-endmay comprise, for example, a low-noise amplifier and/or a mixer. Thereceiver front-end may introduce non-linear distortion and/or phasenoise to the signal 119. The non-linearity of the circuit 108 may berepresented as FnlRx which may be, for example, a polynomial, or anexponential (e.g., Rapp model). The non-linearity may incorporate memory(e.g., Voltera series).

The timing pilot recovery and removal circuit 110 may be operable tolock to the timing pilot signal inserted by the pilot insertion circuit105 in order to recover the symbol timing of the received signal. Theoutput 122 may thus comprise the signal 120 minus (i.e. without) thetiming pilot signal. An example implementation of the timing pilotrecovery and removal circuit 110 is described in the United Statespatent application titled “Timing Synchronization for Reception ofHighly-Spectrally-Efficient Communications,” which is incorporatedherein by reference, as set forth above.

The input filter 109 may be operable to adjust the waveform of thepartial response signal 119 to generate partial response signal 120. Theinput filter 109 may comprise, for example, an infinite impulse response(IIR) and/or a finite impulse response (FIR) filter. The number of taps,or “length,” of the input filter 109 is denoted herein as LRx, aninteger. The impulse response of the input filter 109 is denoted hereinas hRx. The number of taps, and/or tap coefficients of the input filter109 may be configured based on: a non-linearity model,

, signal-to-noise ratio (SNR) of signal 120, the number of taps and/ortap coefficients of the Tx partial response filter 104, and/or otherparameters. The number of taps and/or the values of the tap coefficientsof the input filter 109 may be configured such that noise rejection isintentionally compromised (relative to a perfect match filter) in orderto improve performance in the presence of non-linearity. As a result,the input filter 109 may offer superior performance in the presence ofnon-linearity as compared to, for example, a conventional near zeropositive ISI matching filter (e.g., root raised cosine (RRC) matchedfilter). The input filter 109 may be designed as described in one ormore of: the United States patent application titled “Design andOptimization of Partial Response Pulse Shape Filter,” the United Statespatent application titled “Constellation Map Optimization For HighlySpectrally Efficient Communications,” and the United States patentapplication titled “Dynamic Filter Adjustment ForHighly-Spectrally-Efficient Communications,” each of which isincorporated herein by reference, as set forth above.

As utilized herein, the “total partial response (h)” may be equal to theconvolution of hTx and hRx, and, thus, the “total partial responselength (L)” may be equal to LTx+LRx−1. L may, however, be chosen to beless than LTx+LRx−1 where, for example, one or more taps of the Tx pulseshaper 104 and/or the Rx input filter 109 are below a determined level.Reducing L may reduce decoding complexity of the sequence estimation.This tradeoff may be optimized during the design of the system 100.

The equalizer and sequence estimator 112 may be operable to perform anequalization process and a sequence estimation process. Details of anexample implementation of the equalizer and sequence estimator 112 aredescribed below with respect to FIG. 2. The output signal 132 of theequalizer and sequence estimator 112 may be in the symbol domain and maycarry estimated values of corresponding transmitted symbols (and/orestimated values of the corresponding transmitted information bits ofthe Tx_bitstream) of signal 103. Although not depicted, the signal 132may pass through an interleaver en route to the de-mapper 114. Theestimated values may comprise soft-decision estimates, hard-decisionestimates, or both.

The de-mapper 114 may be operable to map symbols to bit sequencesaccording to a selected modulation scheme. For example, for an N-QAMmodulation scheme, the mapper may map each symbol to Log₂(N) bits of theRx_bitstream. The Rx_bitstream may, for example, be output to ade-interleaver and/or an FEC decoder. Alternatively, or additionally,the de-mapper 114 may generate a soft output for each bit, referred asLLR (Log-Likelihood Ratio). The soft output bits may be used by asoft-decoding forward error corrector (e.g., a low-density parity check(LDPC) decoder). The soft output bits may be generated using, forexample, a Soft Output Viterbi Algorithm (SOVA) or similar. Suchalgorithms may use additional information of the sequence decodingprocess including metrics levels of dropped paths and/or estimated bitprobabilities for generating the LLR, where

${{L\; L\;{R(b)}} = {\log( \frac{P_{b}}{1 - P_{b}} )}},$where P_(b) is the probability that bit b=1.

In an example implementation, components of the system upstream of thepulse shaper 104 in the transmitter and downstream of the equalizer andsequence estimator 112 in the receiver may be as found in a conventionalN-QAM system. Thus, through modification of the transmit side physicallayer and the receive side physical layer, aspects of the invention maybe implemented in an otherwise conventional N-QAM system in order toimprove performance of the system in the presence of non-linearity ascompared, for example, to use of RRC filters and an N-QAM slicer.

FIG. 2 is a block diagram depicting an example equalization and sequenceestimation circuit for use in a system configured for low-complexity,highly-spectrally-efficient communications. Shown are an equalizercircuit 202, a signal combiner circuit 204, a phase adjust circuit 206,a sequence estimation circuit 210, and non-linearity modeling circuits236 a and 236 b.

The equalizer 202 may be operable to process the signal 122 to reduceISI caused by the channel 107. The output 222 of the equalizer 202 is apartial response domain signal. The ISI of the signal 222 is primarilythe result of the pulse shaper 104 and the input filter 109 (there maybe some residual ISI from multipath, for example, due to use of theleast means square (LMS) approach in the equalizer 202). The errorsignal, 201, fed back to the equalizer 202 is also in the partialresponse domain. The signal 201 is the difference, calculated bycombiner 204, between 222 and a partial response signal 203 that isoutput by non-linearity modeling circuit 236 a. An exampleimplementation of the equalizer is described in the United States patentapplication titled “Feed Forward Equalization forHighly-Spectrally-Efficient Communications,” which is incorporatedherein by reference, as set forth above.

The carrier recovery circuit 208 may be operable to generate a signal228 based on a phase difference between the signal 222 and a partialresponse signal 207 output by the non-linearity modeling circuit 236 b.The carrier recovery circuit 208 may be as described in the UnitedStates patent application titled “Coarse Phase Estimation forHighly-Spectrally-Efficient Communications,” which is incorporatedherein by reference, as set forth above.

The phase adjust circuit 206 may be operable to adjust the phase of thesignal 222 to generate the signal 226. The amount and direction of thephase adjustment may be determined by the signal 228 output by thecarrier recovery circuit 208. The signal 226 is a partial responsesignal that approximates (up to an equalization error caused by finitelength of the equalizer 202, a residual phase error not corrected by thephase adjust circuit 206, non-linearities, and/or other non-idealities)the total partial response signal resulting from corresponding symbolsof signal 103 passing through pulse shaper 104 and input filter 109.

The buffer 212 buffers samples of the signal 226 and outputs a pluralityof samples of the signal 226 via signal 232. The signal 232 is denotedPR1, where the underlining indicates that it is a vector (in this caseeach element of the vector corresponds to a sample of a partial responsesignal). In an example implementation, the length of the vector PR1 maybe Q samples.

Input to the sequence estimation circuit 210 are the signal 232, thesignal 228, and a response ĥ. Response ĥ is based on h (the totalpartial response, discussed above). For example, response ĥ mayrepresent a compromise between h (described above) and a filter responsethat compensates for channel non-idealities such as multi-path. Theresponse ĥ may be conveyed and/or stored in the form of LTx+LRx−1 tapcoefficients resulting from convolution of the LTx tap coefficients ofthe pulse shaper 104 and the LRx tap coefficients of the input filter109. Alternatively, response ĥ may be conveyed and/or stored in the formof fewer than LTx+LRx−1 tap coefficientsfor example, where one or moretaps of the LTx and LRx is ignored due to being below a determinedthreshold. The sequence estimation circuit 210 may output partialresponse feedback signals 205 and 209, a signal 234 that corresponds tothe finely determined phase error of the signal 120, and signal 132(which carries hard and/or soft estimates of transmitted symbols and/ortransmitted bits). An example implementation of the sequence estimationcircuit 210 is described below with reference to FIG. 3.

The non-linear modeling circuit 236 a may apply a non-linearity function

(a model of the non-linearity seen by the received signal en route tothe circuit 210) to the signal 205 resulting in the signal 203.Similarly, the non-linear modeling circuit 236 b may apply thenon-linearity function

to the signal 209 resulting in the signal 207.

may be, for example, a third-order or fifth-order polynomial. Increasedaccuracy resulting from the use of a higher-order polynomial for

may tradeoff with increased complexity of implementing a higher-orderpolynomial. Where FnlTx is the dominant non-linearity of thecommunication system 100,

modeling only FnlTx may be sufficient. Where degradation in receiverperformance is above a threshold due to other non-linearities in thesystem (e.g., non-linearity of the receiver front-end 108) the model

may take into account such other non-linearities

FIG. 3 is a block diagram depicting an example sequence estimationcircuit for use in a system configured for low-complexity,highly-spectrally-efficient communications. Shown are a candidategeneration circuit 302, a metrics calculation circuit 304, a candidateselection circuit 306, a combiner circuit 308, a buffer circuit 310, abuffer circuit 312, a phase adjust circuit 314, and convolution circuits316 a and 316 b. The sequence estimation process described with respectto FIG. 3 is an example only. Many variations of the sequence estimationprocess are also possible. For example, although the implementationdescribed here uses one phase survivor per symbol survivor, anotherimplementation may have PSu (e.g., PSu<Su) phase survivors that will beused commonly for each symbol survivor.

For each symbol candidate at time n, the metrics calculation circuit 304may be operable to generate a metric vector D_(n) ¹ . . . D_(n)^(M×Su×P) based on the partial response signal PR1, the signal 303 aconveying the phase candidate vectors PC_(n) ¹ . . . PC_(n) ^(M×Su×P),and the signal 303 b conveying the symbol candidate vectors SC_(n) ¹ . .. SC_(n) ^(M×Su×P), where underlining indicates a vector, subscript nindicates that it is the candidate vectors for time n, M is an integerequal to the size of the symbol alphabet (e.g., for N-QAM, M is equal toN), Su is an integer equal to the number of symbol survivor vectorsretained for each iteration of the sequence estimation process, and P isan integer equal to the size of the phase alphabet. In an exampleimplementation, the size of phase alphabet is three, with each of thethree symbols corresponding to one of: a positive shift, a negativephase shift, or zero phase shift, as further described below withrespect to FIGS. 5A-5E and in the United States patent applicationtitled “Fine Phase Estimation for Highly Spectrally EfficientCommunications,” which is incorporated herein by reference, as set forthabove. In an example implementation, each phase candidate vector maycomprise Q phase values and each symbol candidate vector may comprise Qsymbols. An example implementation of the metrics calculation block isdescribed below with reference to FIG. 4.

The candidate selection circuit 306 may be operable to select Su of thesymbol candidates SC_(n) ¹ . . . SC_(n) ^(M×Su×P) and Su of the phasecandidates PC_(n) ¹ . . . PC_(n) ^(M×Su×P) based on the metrics D_(n) ¹. . . D_(n) ^(M×Su×P). The selected phase candidates are referred to asthe phase survivors PS_(n) ¹ . . . PS_(n) ^(Su). Each element of eachphase survivors PS_(n) ¹ . . . PS_(n) ^(Su) may correspond to anestimate of residual phase error in the signal 232. That is, the phaseerror remaining in the signal after coarse phase error correction viathe phase adjust circuit 206. The best phase survivor PS_(n) ¹ isconveyed via signal 307 a. The Su phase survivors are retained for thenext iteration of the sequence estimation process (at which time theyare conveyed via signal 301 b). The selected symbol candidates arereferred to as the symbol survivors SS_(n) ¹ . . . SS_(n) ^(Su). Eachelement of each symbol survivors SS_(n) ¹ . . . SS_(n) ^(Su) maycomprise a soft-decision estimate and/or a hard-decision estimate of asymbol and/or information bits of the signal 232. The best symbolsurvivor SS_(n) ¹ is conveyed to symbol buffer 310 via the signal 307 b.The Su symbol survivors are retained for the next iteration of thesequence estimation process (at which time they are conveyed via signal301 a). Although, the example implementation described selects the samenumber, Su, of phase survivors and symbol survivors, such is notnecessarily the case. Operation of example candidate selection circuits306 are described below with reference to FIGS. 5D and 6A-6B.

The candidate generation circuit 302 may be operable to generate phasecandidates PC_(n) ¹ . . . PC_(n) ^(M×Su×P) and symbol candidates SC_(n)¹ . . . SC_(n) ^(M×Su×P) from phase survivors PS_(n-1) ¹ . . . PS_(n-1)^(Su) and symbol survivors SS_(n-1) ¹ . . . SS_(n-1) ^(Su), wherein theindex n−1 indicates that they are survivors from time n−1 are used forgenerating the candidates for time n. In an example implementation,generation of the phase and/or symbol candidates may be as, for example,described below with reference to FIGS. 5A-5C and/or in the UnitedStates patent application titled “Low-Complexity,Highly-Spectrally-Efficient Communications,” which is incorporatedherein by reference, as set forth above.

The symbol buffer circuit 310 may comprise a plurality of memoryelements operable to store one or more symbol survivor elements of oneor more symbol survivor vectors. The phase buffer circuit 312 maycomprise a plurality of memory elements operable to store one or morephase survivor vectors. Example implementations of the buffers 310 and312 are described in the United States patent application titled“Low-Complexity, Highly-Spectrally-Efficient Communications,” which isincorporated herein by reference, as set forth above.

The combiner circuit 308 may be operable to combine the best phasesurvivor, PS_(n) ¹, conveyed via signal 307 a, with the signal 228generated by the carrier recovery circuit 208 (FIG. 2) to generate finephase error vector FPE_(n) ¹, conveyed via signal 309, which correspondsto the finely estimated phase error of the signal 222 (FIG. 2). At eachtime n, fine phase error vector FPE_(n-1) ¹ stored in phase buffer 312may be overwritten by FPE_(n) ¹.

The phase adjust circuit 314 may be operable to adjust the phase of thesignal 315 a by an amount determined by the signal 234 output by phasebuffer 312, to generate the signal 205.

The circuit 316 a, which performs a convolution, may comprise a FIRfilter or IIR filter, for example. The circuit 316 a may be operable toconvolve the signal 132 with response, resulting in the partial responsesignal 315 a. Similarly, the convolution circuit 316 b may be operableto convolve the signal 317 with response ĥ, resulting in the partialresponse signal 209. As noted above, response ĥ may be stored by, and/orconveyed to, the sequence estimation circuit 210 in the form of one ormore tap coefficients, which may be determined based on the tapcoefficients of the pulse shaper 104 and/or input filter 109 and/orbased on an adaptation algorithm of a decision feedback equalizer (DFE).Response ĥ may thus represent a compromise between attempting toperfectly reconstruct the total partial response signal (103 as modifiedby pulse shaper 104 and input filter 109) on the one hand, andcompensating for multipath and/or other non-idealities of the channel107 on the other hand. In this regard, the system 100 may comprise oneor more DFEs as described in one or more of: the United States patentapplication titled “Decision Feedback Equalizer forHighly-Spectrally-Efficient Communications,” the United States patentapplication titled “Decision Feedback Equalizer with Multiple Cores forHighly-Spectrally-Efficient Communications,” and the United Statespatent application titled “Decision Feedback Equalizer Utilizing SymbolError Rate Biased Adaptation Function for Highly-Spectrally-EfficientCommunications,” each of which is incorporated herein by reference, asset forth above.

Thus, signal 203 is generated by taking a first estimate of transmittedsymbols, (an element of symbol survivor SS_(n) ¹), converting the firstestimate of transmitted symbols to the partial response domain viacircuit 316 a, and then compensating for non-linearity in thecommunication system 100 via circuit 236 a (FIG. 2). Similarly, signal207 is generated from a second estimate of transmitted symbols (anelement of symbol survivor SS_(n) ¹) that is converted to the partialresponse domain by circuit 316 b to generate signal 209, and thenapplying a non-linear model to the signal 209 b to compensate fornon-linearity in the signal path.

FIG. 4 is a block diagram depicting an example metrics calculationcircuit for use in a system configured for low-complexity,highly-spectrally-efficient communications. Shown is a phase adjustcircuit 402, a convolution circuit 404, a cost function calculationcircuit 406, and non-linear modeling circuit 408. The phase adjustcircuit 402 may phase shift one or more elements of the vector PR1(conveyed via signal 232) by a corresponding one or more values of thephase candidate vectors PC_(n) ¹ . . . PC_(n) ^(M×Su×P). The signal 403output by the phase adjust circuit 402 thus conveys a plurality ofpartial response vectors PR2_(n) ¹ . . . PR2_(n) ^(M×Su×P), each ofwhich comprises a plurality of phase-adjusted versions of PR1.

The circuit 404, which performs a convolution, may comprise a FIR filteror IIR filter, for example. The circuit 404 may be operable to convolvethe symbol candidate vectors SC_(n) ¹ . . . SC_(n) ^(M×Su×P) with ĥ. Thesignal 405 output by the circuit 404 thus conveys vectors SCPR_(n) ¹ . .. SCPR_(n) ^(M×Su×P), each of which is a candidate partial responsevector. The disclosure, however, may not limited to application ofconvolution during sequence estimation, which (the convolution) be onlya particular approach used in instances where the system is configuredfor partial response based communication. In general, linear combinationmay be applied (e.g., in the form of matrix multiplication) between thecandidate vectors SC_(n) ¹ . . . SC_(n) ^(M×Su×P) and a correspondingplurality of linear combination weights. In other words, linearcombination (e.g., matrix multiplications) may be associated with useISC signals at large, while convolution may be particularly associatedwith partial response signals. This claim covers ISC signals—i.e. theconvolution of symbols with partial response taps may be equivalent toan application of linear combination of symbols with the filter tapsbeing the linear combination weights.

The non-linear modeling circuit 408 may apply the non-linearity function

(e.g., model of the non-linearity seen by the received signal en routeto the circuit 210) to the signal 405 resulting in the signal 407. Thesignal 407 output by the circuit 408 thus conveys vectors SCPRNL_(n) ¹ .. . SCPRNL_(n) ^(M×Su×P), each of which is a non-linear adjustedcandidate partial response vector.

Metrics related to the sequence estimation candidates may be accumulatedat each iteration with the candidate branch metric being calculated forthe new received sample. In instances where the non-linear modelincorporates memory (e.g., the outcome of the model output may be afunction of previous partial response samples) the metric may be updatedregressively. For example, assuming that the non-linear model has memoryof order 1 (i.e. the output of the non-linear model depends on thecurrent input and the previous one), the metric update may need toregressively modify the previous branch metric to reflect the memorydepth on 1. In other words, in instances where the memory depth of thenon-linear model is m, at each iteration the metric associated with anygiven candidate should be updated such that to regress m previous branchmetrics along with the new metric related to the new coming sample.

The cost function circuit 406 may be operable to generate metricsindicating the similarity between one or more of the partial responsevectors PR2_(n) ¹ . . . PR2_(n) ^(M×Su×P) and one or more of the vectorsSCPRNL_(n) ¹ . . . SCPRNL_(n) ^(M×Su×P) to generate error metrics D_(n)¹ . . . D_(n) ^(M×Su×P). In an example implementation, the error metricsmay be Euclidean distances calculated as shown below in equation 1.D _(n) ^(i)=|(SCPRNL _(n) ^(i))−(PR2_(n) ^(i))|²  EQ. 1for 1≦i≦M×Su×P.

FIGS. 5A-5E depict portions of an example sequence estimation processperformed by a system configured for joint sequence estimation of symboland phase with high tolerance of nonlinearity. In FIGS. 5A-5E it isassumed, for purposes of illustration, that M=4 (a symbol alphabet of α,β, χ, δ), Su=3 (three symbol survivors are selected each iteration),Psu=Su (three phase survivors are selected each iteration), P=3 (a phasealphabet of plus, minus, and zero), and that Q (vector length) is 4.

Referring to FIG. 5A, there is shown phase and symbol survivors fromtime n−1 on the left side of the figure. The first step in generatingsymbol candidates and phase candidates from the survivors, with hightolerance of nonlinearity, is to duplicate the survivors, shift thecontents in each of the resulting vectors called out as 502 on the rightside of FIG. 5A, and additionally, for each of the symbol vectors,insert ‘0’ in the vacant element(s). In the example implementationdepicted, the survivors are duplicated M*P−1 times and shifted oneelement, with ‘0’ inserted in the right-most elements of the symbolvectors.

Referring to FIG. 5B, the next step in generating the candidates isinserting symbol values in the symbol vectors and phase values in thephase vectors, resulting in the vectors, SC_(n), and phase candidates,PC_(n) for time n (called out as 504 in FIG. 5B). In this regard, forthe phase vectors, the phase values are inserted in the vacant elementsof the phase vectors. For the symbol vectors, however, the symbol valuesare inserted in the [n−1] element rather than the [n] element of thesymbol vectors.

Insertion of the symbol values into the [n−1] elements rather than the[n] element of the symbol vector may enhance estimation process in lightof the use of partial response pulse shaping, and in light of thepresence of nonlinearities in the transmitter and/or receivers. In thisregard, because partial response signals are generated by applying aconvolution function between the partial response filter taps and themapped symbols, any symbol may typically affect a number of samplesequal to the length of the partial response. The (unknown) most-recentsymbol which may be up for estimation, however, may affect only themost-recent received sample. The contribution of the most-recent symbolis factored by the earliest partial response filter tap which may beconfigured to have relatively low amplitude in order to allow optimalpulse shaping as described, for example, in the United States patentapplication titled “Design and Optimization of Partial Response PulseShape Filter,” which is incorporated herein by reference, as set forthabove” which is hereby incorporated herein by reference in its entirety.Therefore, the impact of the most-recent symbol on the most-recentsample of the received signal may be small. Consequently, estimation ofthe most-recent symbol may be susceptible to even low levels of noise orinterference—e.g., even a low level of AWGN may cause error inestimating the most-recent symbol. Errors in estimating the most-recentsymbol may, in turn, impact the estimation of subsequent symbols andlead to an error burst. Thus, due to the possible low reliability inestimating the most-recent symbol, and the fact that the sequenceestimation may be limited to M*Su candidates, which are very smallsubset of the state space, M^(L−1), the survivors selection may lead toerror bursts that may not otherwise occur with full MLSE search.Accordingly, to improve sequence estimation performance withoutincreasing number of survivors (which would increase complexity), thebranch metrics may calculated for the 2^(nd) element (i.e. the [n−1]element) in each symbol candidate, which may actually be the previousunknown symbol. In order to calculate such metrics, however, a “filler”value may need to be populated in the 1^(st) element of the candidatevectors such that the metrics are a fair comparison between thecandidates. Accordingly, the filler values may be determined using, forexample, inverse calculation for each survivor candidate to satisfy thecost function. The filler values may be calculated by, for example, thesequence estimation circuit 112. Inverse calculation is described inmore detail with respect to FIG. 5C (below). Because inverse calculationmay perform lower than the Maximum Likelihood (thus may causedegradation to the overall error rate), it may be necessary to repeatthe estimation of symbol (for the 1^(st) element) using a search. Inother words, the filler value is used only for calculating the branchmetric during this iteration and then is discarded and/or overwritten inthe next iteration. For example, in FIG. 5A, the α in the 1^(st) elementof SS_(n-1) ¹, the α in the 1^(st) element of SS_(n-1) ², and β in the1^(st) element of SS_(n-1) ³ may have each been filler values which arethen discarded in FIG. 5B.

In the example implementation depicted, each of the M possible symbolvalues is inserted into Su*P symbol candidates at element [n−1] of thesymbol vectors, and each of the P phase values may be inserted into M*Sucandidates, at the vacant [n] element. In this regard, in the exampleimplementation depicted, θ5 is a reference phase value calculated basedon phase survivor PS_(n-1) ¹. For example, θ5 may be the average (or aweighted average) of the last two or more elements of the phase survivorPS_(n-1) ¹ (in the example shown, the average over the last two elementswould be (θ5+0)/2). In the example implementation depicted, θ4=θ5−Δθ,and θ6=θ5+Δθ, where Δθ is based on: the amount of phase noise in signal226, slope (derivative) of the phase noise in signal 226,signal-to-noise ratio (SNR) of signal 226, and/or capacity of thechannel 107. Similarly, in the example implementation shown, θ8 is areference phase value calculated based on phase survivor PS_(n-1) ²,θ7=θ8−Δθ, θ9=θ8+Δθ, θ11 is a reference phase value calculated based onphase survivor PS_(n-1) ³, θ10=θ11−Δθ, and θ2=θ11+Δθ.

Referring to FIG. 5C, the next step is generating filler values for then^(th) elements in the symbol vectors (i.e. for insertion into elements[n] in the symbol vectors), resulting in the symbol candidates SC_(n) ¹. . . SC_(n) ^(M×Su×P) and phase candidates PC_(n) ¹ . . . PC_(n)^(M×Su×P) (shown as 506 in FIG. 5C). In this regard, the symbolestimates for the n^(th) elements may be calculated based on best matchwith the received signal for purposes of making a fair comparisonbetween the candidates.

The generation of the symbol estimates may be calculated to minimizecost function, using inverse calculation (per each candidate). In thisregard, the symbol estimate calculation may be based on, for example,the symbols, partial response, and noise. For example, assuming a linearchannel, the partial response received signal can be expressed by:

$x_{n} = {{{\sum\limits_{i = 1}^{N}{a_{n - i} \cdot h_{i}}} + w_{n}} = {{{\underset{\_}{a}}_{n}^{T} \cdot \underset{\_}{h}} + w_{n}}}$where x_(n) is the received signal at the receiver at instant n, h is avector of the tap coefficients of the Tx partial response, a _(n) ^(T)is the transposed transmitted symbols vector (i.e. the transmittedsymbols resulting in x_(n)), and w_(n) is the noise (e.g., additivewhite Gaussian noise or AWGN).

For the linear channel case, the sequence estimation may be configuredto minimize the squared error: |â _(n) ^(T)·ĥ−x_(n)|², where â _(n) ^(T)is the estimated symbols vector which provides the minimal value and ĥis the partial response filter used by the sequence estimation. Assumingcandidate symbol vector ã _(n) ^(T)=[(ã₁, ã₂, . . . , ã_(N)], which hasits most-recent element (ã_(N)) set to zero and its 2^(nd) element(ã_(N-1)) set to one of the possible values of the symbol to beestimated (i.e. assuming a candidate symbol vector that is the transposeof one of the symbol vectors in SC_(n) FIG. 5B), a missing contributionparameter related to â_(N) may be determined to be:

$\frac{x_{n} - {{\overset{\sim}{\underset{\_}{a}}}_{n}^{T} \cdot \hat{\underset{\_}{h}}}}{{\hat{h}}_{1}}$where ĥ₁ correspond to the coefficient of the 1st tap of the partialresponse used for sequence estimation.

Accordingly, the inverse calculation for n^(th) element of the estimatedsymbols vector, â_(N), assuming a linear channel, may be determined by,for example, slicing the contribution parameter according to the symbolconstellation used for the transmitted symbols, as expressed in equation2 (EQ. 2):

${\hat{a}}_{N} = {{slice}\{ \frac{x_{n} - {{\overset{\sim}{\underset{\_}{a}}}_{n}^{T} \cdot \hat{\underset{\_}{h}}}}{{\hat{h}}_{1}} \}}$

In the presence of non-linearities, however, symbol candidate estimationmay need to be configured to specifically account for nonlinearities.Thus, assuming that the distortion (e.g., nonlinear) experienced by thereceived signal is known to the receiver, a model of the non-lineardistortion may be used during sequence estimation such that thenon-linear distortion may be tolerated almost without any degradation(e.g., as determined by SER). In the presence of nonlinearity, Thereceived signal may be expressed as:x _(n) =

{a _(n) ^(T) ·h}+w _(n)where

{·} is the non-linear function. The non-linear model may, for example,be expressed as:

{a _(n) ^(T)·h, a _(n-1) ^(T)·h, . . . , a _(n-L) ^(T)·h}.

The estimation algorithm may be, for example, configured to minimizesquared distance (Euclidian) cost function. The distance may becalculated between the received (equalized) signal samples and thereconstructed signal candidates. The candidate which may minimize thecost function (i.e. the best metrics) becomes the estimation solution(i.e. is selected as a survivor). If the generation of the symbolcandidate does not consider the actual response of the signal (e.g.,including non-linearities), the sequence estimation may converged towrong solution(s). Accordingly, in an example embodiment, the non-linearmodel may be applied for each of the partial response reconstructedcandidates (SCPR_(n) ¹ . . . SCPR_(n) ^(M×Su×P)) prior to applying thecost function calculation (as shown in FIG. 4). Thus, the reconstructedcandidates may experience the same response (e.g., includingnon-linearity) as the received signal and the cost function minimizationmay be precise and achieve solutions comparable to Maximum Likelihood(ML) solutions.

For example, assuming that â _(n) ^(T) is a candidate symbol vector(e.g., one of the symbol candidates SC_(n) ¹ . . . SC_(n) ^(M×Su×P)),then applying the non-linear model to that vector would result in:

{â _(n) ^(T)·ĥ}, the reconstructed partial response signal incorporatingthe non-linear model (e.g., a most-recent sample of one of SCPRNL_(n) ¹. . . SCPRNL_(n) ^(M×Su×P)). The squared error signal (e.g., one ofD_(n) ¹ . . . D_(n) ^(M×Su×P)) may then be revised to the form: |x_(n)−

{â _(n) ^(T)·ĥ}|².

In an example implementation, the combination of the revised sequenceestimation process described above and the incorporation of thenon-linear model may be further adjusted. For example, because thecandidates initially (after 504 of FIG. 5B) have zeros instead of themost-recent symbol, the execution of the non-linear model mayincorporate some error in comparison to a fully symbol populatedcandidates. Assuming that the error is sufficiently small (because ofthe small contribution of the most-recent symbol due to the substantialISI in PR implementations), the error may be corrected using, forexample, linear extrapolation:

f_(NL)(y + Δ y) ≅ f_(NL)(y) + f_(NL)^(′)(y) ⋅ Δ y${\Delta\; y} = \frac{{f_{NL}( {y + {\Delta\; y}} )} - {f_{NL}(y)}}{f_{NL}^{\prime}(y)}$Where f′_(NL)(y) is the slope of the non-linear model f_(NL)(y), bothare known to the receiver.

Assuming that Δy=â_(N)·ĥ₁, which is the contribution of the unknownmost-recent symbol candidate â_(N), and y=ã _(n) ^(T)·ĥ is the knowncontribution of candidate vector ã _(n) ^(T), then the unknownmost-recent symbol under the non-linear model may be determined, asexpressed in equation 3 (EQ. 3), to be:

${\Delta\; y} = {{{\hat{a}}_{N} \cdot {\hat{h}}_{1}} = \frac{x_{n} - {f_{NL}\{ {{\overset{\sim}{\underset{\_}{a}}}_{n}^{T} \cdot \hat{\underset{\_}{h}}} \}}}{f_{NL}^{\prime}\{ {{\overset{\sim}{\underset{\_}{a}}}_{n}^{T} \cdot \hat{\underset{\_}{h}}} \}}}$

Therefore, the value of the most-recent symbol may be the value obtainedby slicing, (according to the symbol constellation in use), the valueobtained from equation 3, as shown in equation 4 (EQ. 4), which togenerate the filler values used in FIG. 5C.

${\hat{a}}_{N} = {{slice}\lbrack \frac{x_{n} - {f_{NL}\{ {{\overset{\sim}{\underset{\_}{a}}}_{n}^{T} \cdot \hat{\underset{\_}{h}}} \}}}{f_{NL}^{\prime}{\{ {\overset{\sim}{\underset{\_}{a}} \cdot \hat{\underset{\_}{h}}} \} \cdot {\hat{h}}_{1}}} \rbrack}$Where:${\overset{\sim}{\underset{\_}{a}}}_{n}^{y} = \lbrack {a_{1}^{y},a_{2}^{y},\ldots\mspace{14mu},a_{n - 1}^{y},0} \rbrack$

Accordingly, the y^(th) symbol vector candidate (e.g., as shown in 506)used to generate the metrics may be expressed as:SC _(n) ^(y) =[a ₁ ^(y), . . . ,Sym^(y) ,â _(n) ^(y)]where Sym^(y) may be one of the M possible symbol values inserted forthe search (e.g., the shifted nth element of the same candidate in theprevious iteration)

Referring to FIG. 5D, with reference to FIG. 4. The symbol candidatesare then transformed to the partial response domain via a convolution(e.g., in circuit 404) and the non-linear model may then be applied toall the candidates (e.g., by non-linearity function

in circuit 408), the reference signal PR1 is phase adjusted, and thenthe metrics D_(n) ¹ . . . D_(n) ^(M×Su×P) are calculated based on thepartial response signals PR2_(n) ¹ . . . PR2_(n) ^(M×Su×P) andSCPRNL_(n) ¹ . . . SCPRNL_(n) ^(M×Su×P).

Referring to FIG. 5E, the metrics calculated in FIG. 5D are used toselect which of the candidates generated in FIG. 5C are selected to bethe survivors for the next iteration of the sequence estimation process.FIG. 5E depicts an example implementation in which the survivors areselected in a single step by simply selecting Su candidatescorresponding to the Su best metrics. In the example implementationdepicted, it is assumed that metric D_(n) ¹⁴ is the best metric, thatD_(n) ¹⁶ is the second best metric, and that D_(n) ³⁰ is the third-bestmetric. Accordingly, symbol candidate SC_(n) ¹⁴ is selected as the bestsymbol survivor, PC_(n) ¹⁴ is selected as the best phase survivor,symbol candidate SC_(n) ¹⁶ is selected as the second-best symbolsurvivor, PC_(n) ¹⁶ is selected as the second-best phase survivor,symbol candidate SC_(n) ³⁰ is selected as the third-best symbolsurvivor, and PC_(n) ³⁰ is selected as the third-best phase survivor.The survivor selection process of FIG. 5E may result in selectingidentical symbol candidates which may be undesirable. An Example ofsurvivor selection process that prevents redundant symbol survivors isdescribed in FIG. 6 and in the United States patent application titled“Low-Complexity, Highly-Spectrally-Efficient Communications,” which isincorporated herein by reference, as set forth above.

FIG. 6 is a flowchart illustrating an example process for sequenceestimation, with high tolerance of nonlinearity, for reception ofpartial response signals. The process begins with block 602 in which afirst partial response vector (e.g., PR1) is input to a vectorcalculation circuit (e.g., circuit 402). In block 604, a plurality ofsecond partial response phase vectors (e.g., PR2_(n) ¹ . . . PR2_(n)^(M×Su×P)) are generated based on the first partial response vector anda plurality of phase candidate vectors (e.g., PC_(n) ¹ . . . PC_(n)^(M×Su×P)). In block 606, a plurality of candidate symbol vectors (e.g.,SC_(n) ¹ . . . SC_(n) ^(M×Su×P)) are convolved with a plurality of tapcoefficients (e.g., tap coefficients corresponding to response ĥ) togenerate a plurality of third partial response symbol vectors (e.g.,SCPR_(n) ¹ . . . SCPR_(n) ^(M×Su×P)). Furthermore, in some instances thenon-linearity model,

, may be applied to the plurality of third partial response symbolvectors to generate a plurality of non-linear adjusted candidate partialresponse vector SCPRNL_(n) ¹ . . . SCPRNL_(n) ^(M×Su×P)). In block 608,metrics (e.g., Euclidean distances between the vectors) are generatedbased on the second partial response phase vectors and the third partialresponse vector are generated (e.g., by circuit 406). In block 610, oneor more of the candidate vectors is selected based on the metricsgenerated in block 608. In block 612, a symbol a best one of thesurvivor vectors (e.g., survivor vector corresponding to the lowestmetric) is output to as an estimated transmitted symbol to a de-mapper.

In an example implementation of this disclosure, a receiver may receivea single-carrier inter-symbol correlated (ISC) signal (e.g., signal 68or signal 120) that was generated by passage of symbols through anon-linear circuit (e.g., circuit 106 and/or circuit 108). The receivermay generate estimated values of the transmitted symbols using asequence estimation process (e.g., implemented by circuit 62) and amodel of non-linear circuit (e.g., implemented by circuit(s) 236 aand/or 236 b). The ISC signal may be a partial response signal generatedvia a partial response filter (e.g., a partial response filtercomprising filter(s) 104 and/or 109). The receiver may generate an ISCfeedback signal (e.g., signal 203), and control an equalizer of thereceiver based on the ISC feedback signal. The receiver may generate anISC feedback signal (e.g., signal 207), and control a carrier circuitbased on the ISC feedback signal.

The sequence estimation process may comprise convolving each one of aplurality of candidate symbol vectors (e.g., each one of vectors SC_(n)¹ . . . SC_(n) ^(M×Su×P)) with a plurality of tap coefficients togenerate a corresponding one of a plurality of first ISC vectors (e.g.,one of vectors SCPR_(n) ¹ . . . SCPR_(n) ^(M×Su×P)). Furthermore, insome instances non-linearity model,

, may be applied to the plurality of first ISC vectors to generate aplurality of non-linear adjusted ISC vectors SCPRNL_(n) ¹ . . .SCPRNL_(n) ^(M×Su×P)). The sequence estimation process may comprisegenerating a plurality of metrics (e.g., metrics D_(n) ¹ . . . D_(n)^(M×Su×P)), each one of the metrics corresponding to the result of acost function calculated using one of the first ISC vectors (e.g.,SCPR_(n) ¹) and a second ISC vector (e.g., PR2_(n) ¹). The plurality oftap coefficients may be based on tap coefficients of a partial responsefilter (e.g., tap coefficients of filter(s) 104 and/or 109). Thesequence estimation process may comprise selecting one of the candidatesymbol vectors (SC_(n) ¹) based on the plurality of metrics. Thesequence estimation process may comprise outputting a symbol of theselected candidate symbol vector (e.g., the symbol at index q2 of symbolcandidate SC_(n) ¹) as one of the estimated values of the transmittedsymbols.

Other implementations may provide a non-transitory computer readablemedium and/or storage medium, and/or a non-transitory machine readablemedium and/or storage medium, having stored thereon, a machine codeand/or a computer program having at least one code section executable bya machine and/or a computer, thereby causing the machine and/or computerto perform the processes as described herein.

Methods and systems disclosed herein may be realized in hardware,software, or a combination of hardware and software. Methods and systemsdisclosed herein may be realized in a centralized fashion in at leastone computing system, or in a distributed fashion where differentelements are spread across several interconnected computing systems. Anykind of computing system or other apparatus adapted for carrying out themethods described herein is suited. A typical combination of hardwareand software may be a general-purpose computing system with a program orother code that, when being loaded and executed, controls the computingsystem such that it carries out methods described herein. Anothertypical implementation may comprise an application specific integratedcircuit (ASIC) or chip with a program or other code that, when beingloaded and executed, controls the ASIC such that is carries out methodsdescribed herein.

While methods and systems have been described herein with reference tocertain implementations, it will be understood by those skilled in theart that various changes may be made and equivalents may be substitutedwithout departing from the scope of the present method and/or system. Inaddition, many modifications may be made to adapt a particular situationor material to the teachings of the present disclosure without departingfrom its scope. Therefore, it is intended that the present method and/orsystem not be limited to the particular implementations disclosed, butthat the present method and/or system will include all implementationsfalling within the scope of the appended claims.

What is claimed is:
 1. A system comprising: a sequence estimationcircuit operable to: generate a plurality of candidate vectors, wherein:each of said plurality of candidate vectors comprises a plurality ofelements ranging from a least-recent element to a most-recent element;each of said plurality of candidate vectors contains, in an elementother than its said most-recent element, a respective one of a pluralityof symbol values to be searched; and each of said plurality of candidatevectors contains, in its said most-recent element, a respective one of acorresponding plurality of filler values; calculate a plurality ofbranch metrics corresponding to the plurality of candidate vectors; andselect, based on said plurality of branch metrics, one of said pluralityof candidate vectors to be output for use by another circuit.
 2. Thesystem of claim 1, wherein: said plurality of candidate vectors consistsof M, an integer, candidate vectors; and each of said plurality ofsymbol values to be searched corresponds to a respective one of M valuesof an M-QAM constellation.
 3. The system of claim 1, wherein, as part ofsaid calculation of said plurality of branch metrics, said sequenceestimation circuit is operable to convolve each of said plurality ofcandidate vectors with a plurality of tap coefficients to generate acorresponding plurality of candidate partial response vectors.
 4. Thesystem of claim 3, wherein, as part of said calculation of saidplurality of branch metrics, said sequence estimation circuit isoperable to apply a non-linearity model to each of said plurality ofcandidate partial response vectors to generate a corresponding one of aplurality of partial response reconstructed candidates.
 5. The system ofclaim 4, wherein, as part of said calculation of said plurality ofbranch metrics, said sequence estimation circuit is operable tocalculate a Euclidean distance between each of said plurality of partialresponse reconstructed candidates and a corresponding one of a pluralityof vectors generated from a signal whose values are to be estimated bysaid sequence estimation circuit.
 6. The system of claim 1, wherein saidsequence estimation circuit is operable to perform an inversecalculation to determine each of said plurality of filler values.
 7. Thesystem of claim 6, wherein said inverse calculation uses a model ofnon-linearity experienced by a signal whose values are to be estimatedby said sequence estimation circuit.
 8. The system of claim 1, wherein:said sequence estimation circuit is operable to determine each of saidplurality of filler values; and for any particular one of said pluralityof candidate vectors, determining a corresponding one of said pluralityof filler values comprises insertion of a zero into said most-recentelement of said particular one of said plurality of candidate vectors togenerate a zero-filled vector.
 9. The system of claim 8, wherein, aspart of said determination of said corresponding one of said pluralityof filler values, said sequence estimation circuit is operable todetermine a contribution of a most-recent symbol of a received signalbased on said zero-filled vector.
 10. The system of claim 9, wherein, aspart of said determination of said contribution of said most-recentsymbol of said received signal, said sequence estimation circuit isoperable to perform a slicing operation.
 11. A method comprising: in asequence estimation circuit of a receiver: generating a plurality ofcandidate vectors, wherein: each of said plurality of candidate vectorscomprises a plurality of elements ranging from a least-recent element toa most-recent element; each of said plurality of candidate vectorscontains, in an element other than its said most-recent element, arespective one of a plurality of symbol values to be searched; and eachof said plurality of candidate vectors contains, in its said most-recentelement, a respective one of a corresponding plurality of filler values;calculating a plurality of branch metrics corresponding to the pluralityof candidate vectors; and selecting, based on said plurality of branchmetrics, one of said plurality of candidate vectors to be output for useby another circuit.
 12. The method of claim 11, wherein: said pluralityof candidate vectors consists of M, an integer, candidate vectors; andeach of said plurality of symbol values to be searched corresponds to arespective one of M values of an M-QAM constellation.
 13. The method ofclaim 11, wherein said calculating of said plurality of branch metricscomprises convolving each of said plurality of candidate vectors with aplurality of tap coefficients to generate a corresponding plurality ofcandidate partial response vectors.
 14. The method of claim 13, whereinsaid calculating said plurality of branch metrics comprises applying anon-linearity model to each of said plurality of candidate partialresponse vectors to generate a corresponding one of a plurality ofpartial response reconstructed candidates.
 15. The method of claim 14,wherein said calculating said plurality of branch metrics comprisescalculating a Euclidean distance between each of said plurality ofpartial response reconstructed candidates and a corresponding one of aplurality of vectors generated from a signal whose values are to beestimated by said sequence estimation circuit.
 16. The system of claim11, comprising performing an inverse calculation to determine each ofsaid plurality of filler values.
 17. The system of claim 16, whereinsaid inverse calculation uses a model of non-linearity experienced by asignal whose values are to be estimated by said sequence estimationcircuit.
 18. The method of claim 11, comprising: determining each ofsaid plurality of filler values, wherein for any particular one of saidplurality of candidate vectors, determining a corresponding one of saidplurality of filler values comprises inserting a zero into saidmost-recent element of said particular one of said plurality ofcandidate vectors to generate a zero-filled vector.
 19. The method ofclaim 18, wherein said determining said corresponding one of saidplurality of filler values comprises determining a contribution of amost-recent symbol of a received signal based on said zero-filledvector.
 20. The method of claim 19, wherein said determining saidcontribution of said most-recent symbol of said received signalcomprises performing a slicing operation.